Hard wall boundary condition

The jellium model of the free-electron gas can account for the increased abundance of alkali metal clusters of a certain size which are observed in mass spectroscopy experiments. This occurrence of so-called magic numbers is related directly to the electronic shell structure of the atomic clusters. Rather than solving the Schrodinger equation self-consistently for jellium clusters, we first consider the two simpler problems of a free-electron gas that is confined either within a sphere of radius, R, or within a cubic box of edge length, L (cf. problem 28 of Sutton (1993)). This corresponds to imposing hard-wall boundary conditions on the electrons, namely... 

The simple hard-wall boundary condition, eqn (5.1), does yield the correct ordering of the energy levels as shown in Fig. 5.1. The only exceptions are the 3s and lh states, which have their sequence reversed compared to that of the self-consistent jellium predictions. Experimentally, the most frequently occurring sodium clusters are indeed Na8 and Na20 as expected from their special stability in Fig. 5.3. 

The temperature instability of a two-dimensional reactive fluid of N hard disks bounded by heat conducting walls has been studied by molecular dynamics simulation. The collision of two hard disks is either elastic or inelastic (exothermic reaction), depending on whether the relative kinetic energy at impact exceeds a prescribed activation barrier. Heat removal is accomplished by using a wall boundary condition involving diffuse and specular reflection of the incident particles. Critical conditions for ignition have been obtained and the observations compared with continuum theory results. Other quantities which can be studied include temperature profiles, ignition times, and the effects of local fluctuations. 

In this work, we use the confined atoms model, with hard walls, to estimate the pressure on confined Ca, Sr, and Ba atoms. With this approach, we will give an upper limit to the pressure, because it is well known that the Dirichlet boundary conditions give an overestimation to this quantity. By using this approach, we obtain the profiles of some electronic properties... 

This review has discussed the phase behavior of polymer blends and symmetric block copolymer melts in thin film geometry, considering mostly films confined between two symmetrical hard walls. Occasionally, also an antisymmetric boundary condition (i.e. one wall prefers component A while the other wall prefers component B) is studied. These boundary conditions sometimes approximate the physically most relevant case, namely a polymeric film on a solid substrate exposed to air or vacuum with a free, fiat surface (Fig. 1). The case where the film as a whole breaks up into droplets (Fig. 2) due to dewetting phenomena is not considered, however, nor did we deal with the formation of islands or holes or terraces in the case of ordered block copolymer films (Fig. 4b-d). 

Mean forces and/or pmf s between macroions mediated by small ions, representing the situation in solution, have been calculated using a variety of boundary conditions a cubic box with periodic boundary conditions [16,17,19,100,101], a cubic box with hard walls [15], one spherical cell [102], two spherical cells [97], and a cylindrical cell [26,28]. The assumption of small higher-order correlation effects implies that the mean force should not strongly depend on (i) the boundary conditions or (ii) the shape of the cell or the box. The latter issue has briefly been examined for the cylindrical cell otherwise these aspects have not yet been analyzed. Finally, the... 

Boundary conditions at the hard wall and free surface are... 

The boundary conditions to be satisfied by equation (l) depend on the interior surface conditions. These conditions could range from acoustically hard walls to those of highly absorbent surfaces which are treated with acoustic insulation materials. At acoustically rigid bundaries... 

A completely different nonstandard technique to obtain a first overview of the equation of state was recently proposed by Addison et al. [269], whereby a gravitation-like potential is applied to the system, and the equilibrium density profile and the concentration profile of the center of mass of the polymers is computed to obtain the osmotic equation of state, fii this sedimentation equilibrium method one hence considers a system in the canonical MVT ensemble using a box of linear dimensions L x L x H, with periodic boundary conditions in x and y directions only, while hard walls are used at z = 0 and at z = H. An external potential is applied everywhere in the system ... 

To explore the pathway for wall-induced crystallization, we performed Monte Carlo simulations in the constant normal-pressure NPx T) ensemble. Here N refers to the number of hard-spheres in the system. The simulation box was rectangular with periodic boundary conditions in the x and y directions. In the z-direction, the system is confined by two flat, hard walls at a distance L. is the component of the pressure tensor perpendicular to the plane wall, and T is the temperature. As our unit of length we used the hard-sphere diameter a. T only sets the energy scale. In the following we always use reduced units. The state of the bulk hard-sphere system is completely specified by its volume fraction cf). The coexistence volume fractions for the bulk fluid and solid phase are known [27] [Pg.193]

The simulation results for this model that will be discussed in the following section were obtained by multithreaded, multicanonical, and parallel tempering Monte Carlo simulations imder the assumption that the peptide only interacts with the surface layer (/= 1). A simulation box of dimension [50 A] with periodic boundary conditions parallel to the substrate was used. In perpendicular direction, peptide mobility is restricted by the Si substrate residing by definition atz = 0. The influence of the wall parallel to the substrate is simply steric, i.e., the atoms experience hard-wall repulsion atz = Zmax = 50 A [340]. 

Statistical thermodynamics and computer simulations showed that the density profiles of hard-sphere and Lennard-J ones fluids normal to a planar interface oscillate about the bulk density with a periodicity of roughly one molecular diameter [1079-1086], The oscillations decay exponentially and extend over a few molecular diameters. In this range, the molecules are ordered in layers. The amplitude and range of density fluctuations depend on the specific boundary condition at the wall and on the size and interaction between the molecules. A steep repulsive wall-fluid... 

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